/*
 * Software License Agreement (BSD License)
 *
 *  Point Cloud Library (PCL) - www.pointclouds.org
 *  Copyright (c) 2010-2012, Willow Garage, Inc.
 *  Copyright (c) 2000-2012 Chih-Chung Chang and Chih-Jen Lin
 *
 *  All rights reserved.
 *
 *  Redistribution and use in source and binary forms, with or without
 *  modification, are permitted provided that the following conditions
 *  are met:
 *
 *   * Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *   * Redistributions in binary form must reproduce the above
 *     copyright notice, this list of conditions and the following
 *     disclaimer in the documentation and/or other materials provided
 *     with the distribution.
 *   * Neither the name of copyright holders nor the names of its
 *     contributors may be used to endorse or promote products derived
 *     from this software without specific prior written permission.
 *
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 *  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 *  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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 *  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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 */

#ifndef _LIBSVM_HPP_
#define _LIBSVM_HPP_

#include <pcl/common/utils.h> // pcl::utils::ignore
#include <pcl/ml/svm.h>

#include <cctype>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdarg>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
int libsvm_version = LIBSVM_VERSION;
using Qfloat = float;
using schar = signed char;
#ifndef min
template <class T>
static inline T
min(T x, T y)
{
  return (x < y) ? x : y;
}

#endif
#ifndef max
template <class T>
static inline T
max(T x, T y)
{
  return (x > y) ? x : y;
}

#endif
template <class T>
static inline void
swap(T& x, T& y)
{
  T t = x;
  x = y;
  y = t;
}

template <class S, class T>
static inline void
clone(T*& dst, S* src, int n)
{
  dst = new T[n];
  memcpy(
      reinterpret_cast<void*>(dst), reinterpret_cast<const void*>(src), sizeof(T) * n);
}

static inline double
powi(double base, int times)
{
  double tmp = base, ret = 1.0;

  for (int t = times; t > 0; t /= 2) {
    if (t % 2 == 1)
      ret *= tmp;

    tmp *= tmp;
  }

  return ret;
}

#define INF HUGE_VAL
#define TAU 1e-12
#define Malloc(type, n) static_cast<type*>(malloc((n) * sizeof(type)))
#define Realloc(var, type, n) static_cast<type*>(realloc(var, (n) * sizeof(type)))

static void
print_string_stdout(const char* s)
{
  fputs(s, stdout);
  fflush(stdout);
}

static void (*svm_print_string)(const char*) = &print_string_stdout;
#if 1
static void
info(const char* fmt, ...)
{
  char buf[BUFSIZ];
  va_list ap;
  va_start(ap, fmt);
  vsprintf(buf, fmt, ap);
  va_end(ap);
  (*svm_print_string)(buf);
}

#else
static void
info(const char* fmt, ...)
{}

#endif

//
// Kernel Cache
//
// l is the number of total data items
// size is the cache size limit in bytes
//

class Cache {

public:
  Cache(int l, long int size);
  ~Cache();

  // request data [0,len)
  // return some position p where [p,len) need to be filled
  // (p >= len if nothing needs to be filled)
  int
  get_data(const int index, Qfloat** data, int len);
  void
  swap_index(int i, int j);

private:
  int l;
  long int size;

  struct head_t {
    head_t *prev, *next; // a circular list
    Qfloat* data;
    int len; // data[0,len) is cached in this entry
  };

  head_t* head;
  head_t lru_head;
  void
  lru_delete(head_t* h);
  void
  lru_insert(head_t* h);
};

Cache::Cache(int l_, long int size_) : l(l_), size(size_)
{
  head = static_cast<head_t*>(calloc(l, sizeof(head_t))); // initialized to 0
  size /= sizeof(Qfloat);
  size -= l * sizeof(head_t) / sizeof(Qfloat);
  size = max(
      size, 2 * static_cast<long int>(l)); // cache must be large enough for two columns
  lru_head.next = lru_head.prev = &lru_head;
}

Cache::~Cache()
{
  for (head_t* h = lru_head.next; h != &lru_head; h = h->next)
    free(h->data);

  free(head);
}

void
Cache::lru_delete(head_t* h)
{
  // delete from current location
  h->prev->next = h->next;
  h->next->prev = h->prev;
}

void
Cache::lru_insert(head_t* h)
{
  // insert to last position
  h->next = &lru_head;
  h->prev = lru_head.prev;
  h->prev->next = h;
  h->next->prev = h;
}

int
Cache::get_data(const int index, Qfloat** data, int len)
{
  head_t* h = &head[index];

  if (h->len)
    lru_delete(h);

  int more = len - h->len;

  if (more > 0) {
    // free old space
    while (size < more) {
      head_t* old = lru_head.next;
      lru_delete(old);
      free(old->data);
      size += old->len;
      old->data = nullptr;
      old->len = 0;
    }

    // allocate new space
    h->data = static_cast<Qfloat*>(realloc(h->data, sizeof(Qfloat) * len));

    size -= more;

    swap(h->len, len);
  }

  lru_insert(h);

  *data = h->data;
  return len;
}

void
Cache::swap_index(int i, int j)
{
  if (i == j)
    return;

  if (head[i].len)
    lru_delete(&head[i]);

  if (head[j].len)
    lru_delete(&head[j]);

  swap(head[i].data, head[j].data);

  swap(head[i].len, head[j].len);

  if (head[i].len)
    lru_insert(&head[i]);

  if (head[j].len)
    lru_insert(&head[j]);

  if (i > j)
    swap(i, j);

  for (head_t* h = lru_head.next; h != &lru_head; h = h->next) {
    if (h->len > i) {
      if (h->len > j)
        swap(h->data[i], h->data[j]);
      else {
        // give up
        lru_delete(h);
        free(h->data);
        size += h->len;
        h->data = nullptr;
        h->len = 0;
      }
    }
  }
}

//
// Kernel evaluation
//
// the static method k_function is for doing single kernel evaluation
// the constructor of Kernel prepares to calculate the l*l kernel matrix
// the member function get_Q is for getting one column from the Q Matrix
//

class QMatrix {

public:
  virtual Qfloat*
  get_Q(int column, int len) const = 0;
  virtual double*
  get_QD() const = 0;
  virtual void
  swap_index(int i, int j) const = 0;
  virtual ~QMatrix() {}
};

class Kernel : public QMatrix {

public:
  Kernel(int l, svm_node* const* x, const svm_parameter& param);
  ~Kernel();

  static double
  k_function(const svm_node* x, const svm_node* y, const svm_parameter& param);
  Qfloat*
  get_Q(int column, int len) const override = 0;
  double*
  get_QD() const override = 0;
  void
  swap_index(int i, int j) const override // no so const...
  {
    swap(x[i], x[j]);

    if (x_square)
      swap(x_square[i], x_square[j]);
  }

protected:
  double (Kernel::*kernel_function)(int i, int j) const;

private:
  const svm_node** x;
  double* x_square;

  // svm_parameter
  const int kernel_type;
  const int degree;
  const double gamma;
  const double coef0;

  static double
  dot(const svm_node* px, const svm_node* py);
  double
  kernel_linear(int i, int j) const
  {
    return dot(x[i], x[j]);
  }

  double
  kernel_poly(int i, int j) const
  {
    return powi(gamma * dot(x[i], x[j]) + coef0, degree);
  }

  double
  kernel_rbf(int i, int j) const
  {
    return std::exp(-gamma * (x_square[i] + x_square[j] - 2 * dot(x[i], x[j])));
  }

  double
  kernel_sigmoid(int i, int j) const
  {
    return std::tanh(gamma * dot(x[i], x[j]) + coef0);
  }

  double
  kernel_precomputed(int i, int j) const
  {
    return x[i][int(x[j][0].value)].value;
  }
};

Kernel::Kernel(int l, svm_node* const* x_, const svm_parameter& param)
: kernel_type(param.kernel_type)
, degree(param.degree)
, gamma(param.gamma)
, coef0(param.coef0)
{
  switch (kernel_type) {

  case LINEAR:
    kernel_function = &Kernel::kernel_linear;
    break;

  case POLY:
    kernel_function = &Kernel::kernel_poly;
    break;

  case RBF:
    kernel_function = &Kernel::kernel_rbf;
    break;

  case SIGMOID:
    kernel_function = &Kernel::kernel_sigmoid;
    break;

  case PRECOMPUTED:
    kernel_function = &Kernel::kernel_precomputed;
    break;
  }

  clone(x, x_, l);

  if (kernel_type == RBF) {
    x_square = new double[l];

    for (int i = 0; i < l; i++)
      x_square[i] = dot(x[i], x[i]);
  }
  else
    x_square = nullptr;
}

Kernel::~Kernel()
{
  delete[] x;
  delete[] x_square;
}

double
Kernel::dot(const svm_node* px, const svm_node* py)
{
  double sum = 0;

  while (px->index != -1 && py->index != -1) {
    if (px->index == py->index) {
      sum += px->value * py->value;
      ++px;
      ++py;
    }
    else {
      if (px->index > py->index)
        ++py;
      else
        ++px;
    }
  }

  return sum;
}

double
Kernel::k_function(const svm_node* x, const svm_node* y, const svm_parameter& param)
{
  switch (param.kernel_type) {

  case LINEAR:
    return dot(x, y);

  case POLY:
    return powi(param.gamma * dot(x, y) + param.coef0, param.degree);

  case RBF: {
    double sum = 0;

    while (x->index != -1 && y->index != -1) {
      if (x->index == y->index) {
        double d = x->value - y->value;
        sum += d * d;
        ++x;
        ++y;
      }
      else {
        if (x->index > y->index) {
          sum += y->value * y->value;
          ++y;
        }
        else {
          sum += x->value * x->value;
          ++x;
        }
      }
    }

    while (x->index != -1) {
      sum += x->value * x->value;
      ++x;
    }

    while (y->index != -1) {
      sum += y->value * y->value;
      ++y;
    }

    return std::exp(-param.gamma * sum);
  }

  case SIGMOID:
    return std::tanh(param.gamma * dot(x, y) + param.coef0);

  case PRECOMPUTED: // x: test (validation), y: SV
    return x[int(y->value)].value;

  default:
    return 0; // Unreachable
  }
}

// An SMO algorithm in Fan et al., JMLR 6(2005), p. 1889--1918
// Solves:
//
// min 0.5(\alpha^T Q \alpha) + p^T \alpha
//
//  y^T \alpha = \delta
//  y_i = +1 or -1
//  0 <= alpha_i <= Cp for y_i = 1
//  0 <= alpha_i <= Cn for y_i = -1
//
// Given:
//
// Q, p, y, Cp, Cn, and an initial feasible point \alpha
// l is the size of vectors and matrices
// eps is the stopping tolerance
//
// solution will be put in \alpha, objective value will be put in obj
//

class Solver {

public:
  Solver(){};

  virtual ~Solver(){};

  struct SolutionInfo {
    double obj;
    double rho;
    double upper_bound_p;
    double upper_bound_n;
    double r; // for Solver_NU
  };

  void
  Solve(int l,
        const QMatrix& Q,
        const double* p_,
        const schar* y_,
        double* alpha_,
        double Cp,
        double Cn,
        double eps,
        SolutionInfo* si,
        int shrinking);

protected:
  int active_size;
  schar* y;
  double* G; // gradient of objective function
  enum { LOWER_BOUND, UPPER_BOUND, FREE };
  char* alpha_status; // LOWER_BOUND, UPPER_BOUND, FREE
  double* alpha;
  const QMatrix* Q;
  const double* QD;
  double eps;
  double Cp, Cn;
  double* p;
  int* active_set;
  double* G_bar; // gradient, if we treat free variables as 0
  int l;
  bool unshrink; // XXX

  double
  get_C(int i)
  {
    return (y[i] > 0) ? Cp : Cn;
  }

  void
  update_alpha_status(int i)
  {
    if (alpha[i] >= get_C(i))
      alpha_status[i] = UPPER_BOUND;
    else if (alpha[i] <= 0)
      alpha_status[i] = LOWER_BOUND;
    else
      alpha_status[i] = FREE;
  }

  bool
  is_upper_bound(int i)
  {
    return alpha_status[i] == UPPER_BOUND;
  }

  bool
  is_lower_bound(int i)
  {
    return alpha_status[i] == LOWER_BOUND;
  }

  bool
  is_free(int i)
  {
    return alpha_status[i] == FREE;
  }

  void
  swap_index(int i, int j);
  void
  reconstruct_gradient();
  virtual int
  select_working_set(int& i, int& j);
  virtual double
  calculate_rho();
  virtual void
  do_shrinking();

private:
  bool
  be_shrunk(int i, double Gmax1, double Gmax2);
};

void
Solver::swap_index(int i, int j)
{
  Q->swap_index(i, j);
  swap(y[i], y[j]);
  swap(G[i], G[j]);
  swap(alpha_status[i], alpha_status[j]);
  swap(alpha[i], alpha[j]);
  swap(p[i], p[j]);
  swap(active_set[i], active_set[j]);
  swap(G_bar[i], G_bar[j]);
}

void
Solver::reconstruct_gradient()
{
  // reconstruct inactive elements of G from G_bar and free variables

  if (active_size == l)
    return;

  int nr_free = 0;

  for (int j = active_size; j < l; j++)
    G[j] = G_bar[j] + p[j];

  for (int j = 0; j < active_size; j++)
    if (is_free(j))
      nr_free++;

  if (2 * nr_free < active_size)
    info("\nWARNING: using -h 0 may be faster\n");

  if (nr_free * l > 2 * active_size * (l - active_size)) {
    for (int i = active_size; i < l; i++) {
      const Qfloat* Q_i = Q->get_Q(i, active_size);

      for (int j = 0; j < active_size; j++)
        if (is_free(j))
          G[i] += alpha[j] * Q_i[j];
    }
  }
  else {
    for (int i = 0; i < active_size; i++)
      if (is_free(i)) {
        const Qfloat* Q_i = Q->get_Q(i, l);
        double alpha_i = alpha[i];

        for (int j = active_size; j < l; j++)
          G[j] += alpha_i * Q_i[j];
      }
  }
}

void
Solver::Solve(int l,
              const QMatrix& Q,
              const double* p_,
              const schar* y_,
              double* alpha_,
              double Cp,
              double Cn,
              double eps,
              SolutionInfo* si,
              int shrinking)
{
  this->l = l;
  this->Q = &Q;
  QD = Q.get_QD();
  clone(p, p_, l);
  clone(y, y_, l);
  clone(alpha, alpha_, l);
  this->Cp = Cp;
  this->Cn = Cn;
  this->eps = eps;
  unshrink = false;

  // initialize alpha_status
  {
    alpha_status = new char[l];

    for (int i = 0; i < l; i++)
      update_alpha_status(i);
  }

  // initialize active set (for shrinking)
  {
    active_set = new int[l];

    for (int i = 0; i < l; i++)
      active_set[i] = i;

    active_size = l;
  }

  // initialize gradient
  {
    G = new double[l];
    G_bar = new double[l];

    for (int i = 0; i < l; i++) {
      G[i] = p[i];
      G_bar[i] = 0;
    }

    for (int i = 0; i < l; i++)
      if (!is_lower_bound(i)) {
        const Qfloat* Q_i = Q.get_Q(i, l);
        double alpha_i = alpha[i];

        for (int j = 0; j < l; j++)
          G[j] += alpha_i * Q_i[j];

        if (is_upper_bound(i))
          for (int j = 0; j < l; j++)
            G_bar[j] += get_C(i) * Q_i[j];
      }
  }

  // optimization step

  int iter = 0;
  int max_iter = max(10000000, l > INT_MAX / 100 ? INT_MAX : 100 * l);
  int counter = min(l, 1000) + 1;

  while (iter < max_iter) {
    // show progress and do shrinking

    if (--counter == 0) {
      counter = min(l, 1000);

      if (shrinking)
        do_shrinking();

      info(".");
    }

    int i, j;

    if (select_working_set(i, j) != 0) {
      // reconstruct the whole gradient
      reconstruct_gradient();
      // reset active set size and check
      active_size = l;
      info("*");

      if (select_working_set(i, j) != 0)
        break;
      counter = 1; // do shrinking next iteration
    }

    ++iter;

    // update alpha[i] and alpha[j], handle bounds carefully

    const Qfloat* Q_i = Q.get_Q(i, active_size);
    const Qfloat* Q_j = Q.get_Q(j, active_size);

    double C_i = get_C(i);
    double C_j = get_C(j);

    double old_alpha_i = alpha[i];
    double old_alpha_j = alpha[j];

    if (y[i] != y[j]) {
      double quad_coef = QD[i] + QD[j] + 2 * Q_i[j];

      if (quad_coef <= 0)
        quad_coef = TAU;

      double delta = (-G[i] - G[j]) / quad_coef;

      double diff = alpha[i] - alpha[j];

      alpha[i] += delta;

      alpha[j] += delta;

      if (diff > 0) {
        if (alpha[j] < 0) {
          alpha[j] = 0;
          alpha[i] = diff;
        }
      }
      else {
        if (alpha[i] < 0) {
          alpha[i] = 0;
          alpha[j] = -diff;
        }
      }

      if (diff > C_i - C_j) {
        if (alpha[i] > C_i) {
          alpha[i] = C_i;
          alpha[j] = C_i - diff;
        }
      }
      else {
        if (alpha[j] > C_j) {
          alpha[j] = C_j;
          alpha[i] = C_j + diff;
        }
      }
    }
    else {
      double quad_coef = QD[i] + QD[j] - 2 * Q_i[j];

      if (quad_coef <= 0)
        quad_coef = TAU;

      double delta = (G[i] - G[j]) / quad_coef;

      double sum = alpha[i] + alpha[j];

      alpha[i] -= delta;

      alpha[j] += delta;

      if (sum > C_i) {
        if (alpha[i] > C_i) {
          alpha[i] = C_i;
          alpha[j] = sum - C_i;
        }
      }
      else {
        if (alpha[j] < 0) {
          alpha[j] = 0;
          alpha[i] = sum;
        }
      }

      if (sum > C_j) {
        if (alpha[j] > C_j) {
          alpha[j] = C_j;
          alpha[i] = sum - C_j;
        }
      }
      else {
        if (alpha[i] < 0) {
          alpha[i] = 0;
          alpha[j] = sum;
        }
      }
    }

    // update G

    double delta_alpha_i = alpha[i] - old_alpha_i;

    double delta_alpha_j = alpha[j] - old_alpha_j;

    for (int k = 0; k < active_size; k++) {
      G[k] += Q_i[k] * delta_alpha_i + Q_j[k] * delta_alpha_j;
    }

    // update alpha_status and G_bar

    {
      bool ui = is_upper_bound(i);
      bool uj = is_upper_bound(j);
      update_alpha_status(i);
      update_alpha_status(j);

      if (ui != is_upper_bound(i)) {
        Q_i = Q.get_Q(i, l);

        if (ui)
          for (int k = 0; k < l; k++)
            G_bar[k] -= C_i * Q_i[k];
        else
          for (int k = 0; k < l; k++)
            G_bar[k] += C_i * Q_i[k];
      }

      if (uj != is_upper_bound(j)) {
        Q_j = Q.get_Q(j, l);

        if (uj)
          for (int k = 0; k < l; k++)
            G_bar[k] -= C_j * Q_j[k];
        else
          for (int k = 0; k < l; k++)
            G_bar[k] += C_j * Q_j[k];
      }
    }
  }

  if (iter >= max_iter) {
    if (active_size < l) {
      // reconstruct the whole gradient to calculate objective value
      reconstruct_gradient();
      active_size = l;
      info("*");
    }

    info("\nWARNING: reaching max number of iterations");
  }

  // calculate rho

  si->rho = calculate_rho();

  // calculate objective value
  {
    double v = 0;

    for (int i = 0; i < l; i++)
      v += alpha[i] * (G[i] + p[i]);

    si->obj = v / 2;
  }

  // put back the solution
  {
    for (int i = 0; i < l; i++)
      alpha_[active_set[i]] = alpha[i];
  }

  // juggle everything back
  /*{
   for(int i=0;i<l;i++)
    while(active_set[i] != i)
     swap_index(i,active_set[i]);
     // or Q.swap_index(i,active_set[i]);
  }*/

  si->upper_bound_p = Cp;

  si->upper_bound_n = Cn;

  info("\noptimization finished, #iter = %d\n", iter);

  delete[] p;

  delete[] y;

  delete[] alpha;

  delete[] alpha_status;

  delete[] active_set;

  delete[] G;

  delete[] G_bar;
}

// return 1 if already optimal, return 0 otherwise
int
Solver::select_working_set(int& out_i, int& out_j)
{
  // return i,j such that
  // i: maximizes -y_i * grad(f)_i, i in I_up(\alpha)
  // j: minimizes the decrease of obj value
  //    (if quadratic coefficeint <= 0, replace it with tau)
  //    -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)

  double Gmax = -INF;
  double Gmax2 = -INF;
  int Gmax_idx = -1;
  int Gmin_idx = -1;
  double obj_diff_min = INF;

  for (int t = 0; t < active_size; t++)
    if (y[t] == +1) {
      if (!is_upper_bound(t))
        if (-G[t] >= Gmax) {
          Gmax = -G[t];
          Gmax_idx = t;
        }
    }
    else {
      if (!is_lower_bound(t))
        if (G[t] >= Gmax) {
          Gmax = G[t];
          Gmax_idx = t;
        }
    }

  int i = Gmax_idx;

  const Qfloat* Q_i = nullptr;

  if (i != -1) // NULL Q_i not accessed: Gmax=-INF if i=-1
    Q_i = Q->get_Q(i, active_size);

  for (int j = 0; j < active_size; j++) {
    if (y[j] == +1) {
      if (!is_lower_bound(j)) {
        double grad_diff = Gmax + G[j];

        if (G[j] >= Gmax2)
          Gmax2 = G[j];

        if (grad_diff > 0) {
          double obj_diff;
          double quad_coef = QD[i] + QD[j] - 2.0 * y[i] * Q_i[j];

          if (quad_coef > 0)
            obj_diff = -(grad_diff * grad_diff) / quad_coef;
          else
            obj_diff = -(grad_diff * grad_diff) / TAU;

          if (obj_diff <= obj_diff_min) {
            Gmin_idx = j;
            obj_diff_min = obj_diff;
          }
        }
      }
    }
    else {
      if (!is_upper_bound(j)) {
        double grad_diff = Gmax - G[j];

        if (-G[j] >= Gmax2)
          Gmax2 = -G[j];

        if (grad_diff > 0) {
          double obj_diff;
          double quad_coef = QD[i] + QD[j] + 2.0 * y[i] * Q_i[j];

          if (quad_coef > 0)
            obj_diff = -(grad_diff * grad_diff) / quad_coef;
          else
            obj_diff = -(grad_diff * grad_diff) / TAU;

          if (obj_diff <= obj_diff_min) {
            Gmin_idx = j;
            obj_diff_min = obj_diff;
          }
        }
      }
    }
  }

  if (Gmax + Gmax2 < eps)
    return 1;

  out_i = Gmax_idx;

  out_j = Gmin_idx;

  return 0;
}

bool
Solver::be_shrunk(int i, double Gmax1, double Gmax2)
{
  if (is_upper_bound(i)) {
    if (y[i] == +1)
      return (-G[i] > Gmax1);
    return (-G[i] > Gmax2);
  }
  if (is_lower_bound(i)) {
    if (y[i] == +1)
      return (G[i] > Gmax2);
    return (G[i] > Gmax1);
  }
  return (false);
}

void
Solver::do_shrinking()
{
  double Gmax1 = -INF; // max { -y_i * grad(f)_i | i in I_up(\alpha) }
  double Gmax2 = -INF; // max { y_i * grad(f)_i | i in I_low(\alpha) }

  // find maximal violating pair first

  for (int i = 0; i < active_size; i++) {
    if (y[i] == +1) {
      if (!is_upper_bound(i)) {
        if (-G[i] >= Gmax1)
          Gmax1 = -G[i];
      }

      if (!is_lower_bound(i)) {
        if (G[i] >= Gmax2)
          Gmax2 = G[i];
      }
    }
    else {
      if (!is_upper_bound(i)) {
        if (-G[i] >= Gmax2)
          Gmax2 = -G[i];
      }

      if (!is_lower_bound(i)) {
        if (G[i] >= Gmax1)
          Gmax1 = G[i];
      }
    }
  }

  if (!unshrink && Gmax1 + Gmax2 <= eps * 10) {
    unshrink = true;
    reconstruct_gradient();
    active_size = l;
    info("*");
  }

  for (int i = 0; i < active_size; i++)
    if (be_shrunk(i, Gmax1, Gmax2)) {
      active_size--;

      while (active_size > i) {
        if (!be_shrunk(active_size, Gmax1, Gmax2)) {
          swap_index(i, active_size);
          break;
        }

        active_size--;
      }
    }
}

double
Solver::calculate_rho()
{
  double r;
  int nr_free = 0;
  double ub = INF, lb = -INF, sum_free = 0;

  for (int i = 0; i < active_size; i++) {
    double yG = y[i] * G[i];

    if (is_upper_bound(i)) {
      if (y[i] == -1)
        ub = min(ub, yG);
      else
        lb = max(lb, yG);
    }
    else if (is_lower_bound(i)) {
      if (y[i] == +1)
        ub = min(ub, yG);
      else
        lb = max(lb, yG);
    }
    else {
      ++nr_free;
      sum_free += yG;
    }
  }

  if (nr_free > 0)
    r = sum_free / nr_free;
  else
    r = (ub + lb) / 2;

  return r;
}

//
// Solver for nu-svm classification and regression
//
// additional constraint: e^T \alpha = constant
//

class Solver_NU : public Solver {

public:
  Solver_NU() {}

  void
  Solve(int l,
        const QMatrix& Q,
        const double* p,
        const schar* y,
        double* alpha,
        double Cp,
        double Cn,
        double eps,
        SolutionInfo* si,
        int shrinking)
  {
    this->si = si;
    Solver::Solve(l, Q, p, y, alpha, Cp, Cn, eps, si, shrinking);
  }

private:
  SolutionInfo* si;
  int
  select_working_set(int& i, int& j) override;
  double
  calculate_rho() override;
  bool
  be_shrunk(int i, double Gmax1, double Gmax2, double Gmax3, double Gmax4);
  void
  do_shrinking() override;
};

// return 1 if already optimal, return 0 otherwise
int
Solver_NU::select_working_set(int& out_i, int& out_j)
{
  // return i,j such that y_i = y_j and
  // i: maximizes -y_i * grad(f)_i, i in I_up(\alpha)
  // j: minimizes the decrease of obj value
  //    (if quadratic coefficeint <= 0, replace it with tau)
  //    -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)

  double Gmaxp = -INF;
  double Gmaxp2 = -INF;
  int Gmaxp_idx = -1;

  double Gmaxn = -INF;
  double Gmaxn2 = -INF;
  int Gmaxn_idx = -1;

  int Gmin_idx = -1;
  double obj_diff_min = INF;

  for (int t = 0; t < active_size; t++)
    if (y[t] == +1) {
      if (!is_upper_bound(t))
        if (-G[t] >= Gmaxp) {
          Gmaxp = -G[t];
          Gmaxp_idx = t;
        }
    }
    else {
      if (!is_lower_bound(t))
        if (G[t] >= Gmaxn) {
          Gmaxn = G[t];
          Gmaxn_idx = t;
        }
    }

  int ip = Gmaxp_idx;

  int in = Gmaxn_idx;
  const Qfloat* Q_ip = nullptr;
  const Qfloat* Q_in = nullptr;

  if (ip != -1) // NULL Q_ip not accessed: Gmaxp=-INF if ip=-1
    Q_ip = Q->get_Q(ip, active_size);

  if (in != -1)
    Q_in = Q->get_Q(in, active_size);

  for (int j = 0; j < active_size; j++) {
    if (y[j] == +1) {
      if (!is_lower_bound(j)) {
        double grad_diff = Gmaxp + G[j];

        if (G[j] >= Gmaxp2)
          Gmaxp2 = G[j];

        if (grad_diff > 0) {
          double obj_diff;
          double quad_coef = QD[ip] + QD[j] - 2 * Q_ip[j];

          if (quad_coef > 0)
            obj_diff = -(grad_diff * grad_diff) / quad_coef;
          else
            obj_diff = -(grad_diff * grad_diff) / TAU;

          if (obj_diff <= obj_diff_min) {
            Gmin_idx = j;
            obj_diff_min = obj_diff;
          }
        }
      }
    }
    else {
      if (!is_upper_bound(j)) {
        double grad_diff = Gmaxn - G[j];

        if (-G[j] >= Gmaxn2)
          Gmaxn2 = -G[j];

        if (grad_diff > 0) {
          double obj_diff;
          double quad_coef = QD[in] + QD[j] - 2 * Q_in[j];

          if (quad_coef > 0)
            obj_diff = -(grad_diff * grad_diff) / quad_coef;
          else
            obj_diff = -(grad_diff * grad_diff) / TAU;

          if (obj_diff <= obj_diff_min) {
            Gmin_idx = j;
            obj_diff_min = obj_diff;
          }
        }
      }
    }
  }

  if (max(Gmaxp + Gmaxp2, Gmaxn + Gmaxn2) < eps)
    return 1;

  if (y[Gmin_idx] == +1)
    out_i = Gmaxp_idx;
  else
    out_i = Gmaxn_idx;

  out_j = Gmin_idx;

  return 0;
}

bool
Solver_NU::be_shrunk(int i, double Gmax1, double Gmax2, double Gmax3, double Gmax4)
{
  if (is_upper_bound(i)) {
    if (y[i] == +1)
      return (-G[i] > Gmax1);
    return (-G[i] > Gmax4);
  }
  if (is_lower_bound(i)) {
    if (y[i] == +1)
      return (G[i] > Gmax2);

    return (G[i] > Gmax3);
  }
  return (false);
}

void
Solver_NU::do_shrinking()
{
  double Gmax1 = -INF; // max { -y_i * grad(f)_i | y_i = +1, i in I_up(\alpha) }
  double Gmax2 = -INF; // max { y_i * grad(f)_i | y_i = +1, i in I_low(\alpha) }
  double Gmax3 = -INF; // max { -y_i * grad(f)_i | y_i = -1, i in I_up(\alpha) }
  double Gmax4 = -INF; // max { y_i * grad(f)_i | y_i = -1, i in I_low(\alpha) }

  // find maximal violating pair first

  for (int i = 0; i < active_size; i++) {
    if (!is_upper_bound(i)) {
      if (y[i] == +1) {
        if (-G[i] > Gmax1)
          Gmax1 = -G[i];
      }
      else if (-G[i] > Gmax4)
        Gmax4 = -G[i];
    }

    if (!is_lower_bound(i)) {
      if (y[i] == +1) {
        if (G[i] > Gmax2)
          Gmax2 = G[i];
      }
      else if (G[i] > Gmax3)
        Gmax3 = G[i];
    }
  }

  if (!unshrink && max(Gmax1 + Gmax2, Gmax3 + Gmax4) <= eps * 10) {
    unshrink = true;
    reconstruct_gradient();
    active_size = l;
  }

  for (int i = 0; i < active_size; i++)
    if (be_shrunk(i, Gmax1, Gmax2, Gmax3, Gmax4)) {
      active_size--;

      while (active_size > i) {
        if (!be_shrunk(active_size, Gmax1, Gmax2, Gmax3, Gmax4)) {
          swap_index(i, active_size);
          break;
        }

        active_size--;
      }
    }
}

double
Solver_NU::calculate_rho()
{
  int nr_free1 = 0, nr_free2 = 0;
  double ub1 = INF, ub2 = INF;
  double lb1 = -INF, lb2 = -INF;
  double sum_free1 = 0, sum_free2 = 0;

  for (int i = 0; i < active_size; i++) {
    if (y[i] == +1) {
      if (is_upper_bound(i))
        lb1 = max(lb1, G[i]);
      else if (is_lower_bound(i))
        ub1 = min(ub1, G[i]);
      else {
        ++nr_free1;
        sum_free1 += G[i];
      }
    }
    else {
      if (is_upper_bound(i))
        lb2 = max(lb2, G[i]);
      else if (is_lower_bound(i))
        ub2 = min(ub2, G[i]);
      else {
        ++nr_free2;
        sum_free2 += G[i];
      }
    }
  }

  double r1, r2;

  if (nr_free1 > 0)
    r1 = sum_free1 / nr_free1;
  else
    r1 = (ub1 + lb1) / 2;

  if (nr_free2 > 0)
    r2 = sum_free2 / nr_free2;
  else
    r2 = (ub2 + lb2) / 2;

  si->r = (r1 + r2) / 2;

  return (r1 - r2) / 2;
}

//
// Q matrices for various formulations
//

class SVC_Q : public Kernel {

public:
  SVC_Q(const svm_problem& prob, const svm_parameter& param, const schar* y_)
  : Kernel(prob.l, prob.x, param)
  {
    clone(y, y_, prob.l);
    cache = new Cache(prob.l, static_cast<long int>(param.cache_size * (1 << 20)));
    QD = new double[prob.l];

    for (int i = 0; i < prob.l; i++)
      QD[i] = (this->*kernel_function)(i, i);
  }

  Qfloat*
  get_Q(int i, int len) const override
  {
    Qfloat* data;
    int start;

    if ((start = cache->get_data(i, &data, len)) < len) {
      for (int j = start; j < len; j++)
        data[j] = Qfloat(y[i] * y[j] * (this->*kernel_function)(i, j));
    }

    return data;
  }

  double*
  get_QD() const override
  {
    return QD;
  }

  void
  swap_index(int i, int j) const override
  {
    cache->swap_index(i, j);
    Kernel::swap_index(i, j);
    swap(y[i], y[j]);
    swap(QD[i], QD[j]);
  }

  ~SVC_Q()
  {
    delete[] y;
    delete cache;
    delete[] QD;
  }

private:
  schar* y;
  Cache* cache;
  double* QD;
};

class ONE_CLASS_Q : public Kernel {

public:
  ONE_CLASS_Q(const svm_problem& prob, const svm_parameter& param)
  : Kernel(prob.l, prob.x, param)
  {
    cache = new Cache(prob.l, static_cast<long int>(param.cache_size * (1 << 20)));
    QD = new double[prob.l];

    for (int i = 0; i < prob.l; i++)
      QD[i] = (this->*kernel_function)(i, i);
  }

  Qfloat*
  get_Q(int i, int len) const override
  {
    Qfloat* data;
    int start;

    if ((start = cache->get_data(i, &data, len)) < len) {
      for (int j = start; j < len; j++)
        data[j] = Qfloat((this->*kernel_function)(i, j));
    }

    return data;
  }

  double*
  get_QD() const override
  {
    return QD;
  }

  void
  swap_index(int i, int j) const override
  {
    cache->swap_index(i, j);
    Kernel::swap_index(i, j);
    swap(QD[i], QD[j]);
  }

  ~ONE_CLASS_Q()
  {
    delete cache;
    delete[] QD;
  }

private:
  Cache* cache;
  double* QD;
};

class SVR_Q : public Kernel {

public:
  SVR_Q(const svm_problem& prob, const svm_parameter& param)
  : Kernel(prob.l, prob.x, param)
  {
    l = prob.l;
    cache = new Cache(l, static_cast<long int>(param.cache_size * (1 << 20)));
    QD = new double[2 * l];
    sign = new schar[2 * l];
    index = new int[2 * l];

    for (int k = 0; k < l; k++) {
      sign[k] = 1;
      sign[k + l] = -1;
      index[k] = k;
      index[k + l] = k;
      QD[k] = (this->*kernel_function)(k, k);
      QD[k + l] = QD[k];
    }

    buffer[0] = new Qfloat[2 * l];

    buffer[1] = new Qfloat[2 * l];
    next_buffer = 0;
  }

  void
  swap_index(int i, int j) const override
  {
    swap(sign[i], sign[j]);
    swap(index[i], index[j]);
    swap(QD[i], QD[j]);
  }

  Qfloat*
  get_Q(int i, int len) const override
  {
    Qfloat* data;
    int j, real_i = index[i];

    if (cache->get_data(real_i, &data, l) < l) {
      for (j = 0; j < l; j++)
        data[j] = Qfloat((this->*kernel_function)(real_i, j));
    }

    // reorder and copy
    Qfloat* buf = buffer[next_buffer];

    next_buffer = 1 - next_buffer;

    schar si = sign[i];

    for (j = 0; j < len; j++)
      buf[j] = Qfloat(si) * Qfloat(sign[j]) * data[index[j]];

    return buf;
  }

  double*
  get_QD() const override
  {
    return QD;
  }

  ~SVR_Q()
  {
    delete cache;
    delete[] sign;
    delete[] index;
    delete[] buffer[0];
    delete[] buffer[1];
    delete[] QD;
  }

private:
  int l;
  Cache* cache;
  schar* sign;
  int* index;
  mutable int next_buffer;
  Qfloat* buffer[2];
  double* QD;
};

//
// construct and solve various formulations
//
static void
solve_c_svc(const svm_problem* prob,
            const svm_parameter* param,
            double* alpha,
            Solver::SolutionInfo* si,
            double Cp,
            double Cn)
{
  int l = prob->l;
  double* minus_ones = new double[l];
  schar* y = new schar[l];

  for (int i = 0; i < l; i++) {
    alpha[i] = 0;
    minus_ones[i] = -1;

    if (prob->y[i] > 0)
      y[i] = +1;
    else
      y[i] = -1;
  }

  Solver s;

  s.Solve(l,
          SVC_Q(*prob, *param, y),
          minus_ones,
          y,
          alpha,
          Cp,
          Cn,
          param->eps,
          si,
          param->shrinking);

  double sum_alpha = 0;

  for (int i = 0; i < l; i++)
    sum_alpha += alpha[i];

  if (Cp == Cn)
    info("nu = %f\n", sum_alpha / (Cp * prob->l));

  for (int i = 0; i < l; i++)
    alpha[i] *= y[i];

  delete[] minus_ones;

  delete[] y;
}

static void
solve_nu_svc(const svm_problem* prob,
             const svm_parameter* param,
             double* alpha,
             Solver::SolutionInfo* si)
{
  int l = prob->l;
  double nu = param->nu;

  schar* y = new schar[l];

  for (int i = 0; i < l; i++)
    if (prob->y[i] > 0)
      y[i] = +1;
    else
      y[i] = -1;

  double sum_pos = nu * l / 2;

  double sum_neg = nu * l / 2;

  for (int i = 0; i < l; i++)
    if (y[i] == +1) {
      alpha[i] = min(1.0, sum_pos);
      sum_pos -= alpha[i];
    }
    else {
      alpha[i] = min(1.0, sum_neg);
      sum_neg -= alpha[i];
    }

  double* zeros = new double[l];

  for (int i = 0; i < l; i++)
    zeros[i] = 0;

  Solver_NU s;

  s.Solve(l,
          SVC_Q(*prob, *param, y),
          zeros,
          y,
          alpha,
          1.0,
          1.0,
          param->eps,
          si,
          param->shrinking);

  double r = si->r;

  info("C = %f\n", 1 / r);

  for (int i = 0; i < l; i++)
    alpha[i] *= y[i] / r;

  si->rho /= r;

  si->obj /= (r * r);

  si->upper_bound_p = 1 / r;

  si->upper_bound_n = 1 / r;

  delete[] y;

  delete[] zeros;
}

static void
solve_one_class(const svm_problem* prob,
                const svm_parameter* param,
                double* alpha,
                Solver::SolutionInfo* si)
{
  int l = prob->l;
  double* zeros = new double[l];
  schar* ones = new schar[l];

  int n = int(param->nu * prob->l); // # of alpha's at upper bound

  for (int i = 0; i < n; i++)
    alpha[i] = 1;

  if (n < prob->l)
    alpha[n] = param->nu * prob->l - n;

  for (int i = n + 1; i < l; i++)
    alpha[i] = 0;

  for (int i = 0; i < l; i++) {
    zeros[i] = 0;
    ones[i] = 1;
  }

  Solver s;

  s.Solve(l,
          ONE_CLASS_Q(*prob, *param),
          zeros,
          ones,
          alpha,
          1.0,
          1.0,
          param->eps,
          si,
          param->shrinking);

  delete[] zeros;
  delete[] ones;
}

static void
solve_epsilon_svr(const svm_problem* prob,
                  const svm_parameter* param,
                  double* alpha,
                  Solver::SolutionInfo* si)
{
  int l = prob->l;
  double* alpha2 = new double[2 * l];
  double* linear_term = new double[2 * l];
  schar* y = new schar[2 * l];

  for (int i = 0; i < l; i++) {
    alpha2[i] = 0;
    linear_term[i] = param->p - prob->y[i];
    y[i] = 1;

    alpha2[i + l] = 0;
    linear_term[i + l] = param->p + prob->y[i];
    y[i + l] = -1;
  }

  Solver s;

  s.Solve(2 * l,
          SVR_Q(*prob, *param),
          linear_term,
          y,
          alpha2,
          param->C,
          param->C,
          param->eps,
          si,
          param->shrinking);

  double sum_alpha = 0;

  for (int i = 0; i < l; i++) {
    alpha[i] = alpha2[i] - alpha2[i + l];
    sum_alpha += std::abs(alpha[i]);
  }

  info("nu = %f\n", sum_alpha / (param->C * l));

  delete[] alpha2;
  delete[] linear_term;
  delete[] y;
}

static void
solve_nu_svr(const svm_problem* prob,
             const svm_parameter* param,
             double* alpha,
             Solver::SolutionInfo* si)
{
  int l = prob->l;
  double C = param->C;
  double* alpha2 = new double[2 * l];
  double* linear_term = new double[2 * l];
  schar* y = new schar[2 * l];

  double sum = C * param->nu * l / 2;

  for (int i = 0; i < l; i++) {
    alpha2[i] = alpha2[i + l] = min(sum, C);
    sum -= alpha2[i];

    linear_term[i] = -prob->y[i];
    y[i] = 1;

    linear_term[i + l] = prob->y[i];
    y[i + l] = -1;
  }

  Solver_NU s;

  s.Solve(2 * l,
          SVR_Q(*prob, *param),
          linear_term,
          y,
          alpha2,
          C,
          C,
          param->eps,
          si,
          param->shrinking);

  info("epsilon = %f\n", -si->r);

  for (int i = 0; i < l; i++)
    alpha[i] = alpha2[i] - alpha2[i + l];

  delete[] alpha2;

  delete[] linear_term;

  delete[] y;
}

//
// decision_function
//

struct decision_function {
  double* alpha;
  double rho;
};

static decision_function
svm_train_one(const svm_problem* prob, const svm_parameter* param, double Cp, double Cn)
{
  double* alpha = Malloc(double, prob->l);
  Solver::SolutionInfo si;

  switch (param->svm_type) {

  case C_SVC:
    solve_c_svc(prob, param, alpha, &si, Cp, Cn);
    break;

  case NU_SVC:
    solve_nu_svc(prob, param, alpha, &si);
    break;

  case ONE_CLASS:
    solve_one_class(prob, param, alpha, &si);
    break;

  case EPSILON_SVR:
    solve_epsilon_svr(prob, param, alpha, &si);
    break;

  case NU_SVR:
    solve_nu_svr(prob, param, alpha, &si);
    break;
  }

  info("obj = %f, rho = %f\n", si.obj, si.rho);

  // output SVs

  int nSV = 0;
  int nBSV = 0;

  for (int i = 0; i < prob->l; i++) {
    if (std::abs(alpha[i]) > 0) {
      ++nSV;

      if (prob->y[i] > 0) {
        if (std::abs(alpha[i]) >= si.upper_bound_p)
          ++nBSV;
      }
      else {
        if (std::abs(alpha[i]) >= si.upper_bound_n)
          ++nBSV;
      }
    }
  }

  info("nSV = %d, nBSV = %d\n", nSV, nBSV);

  decision_function f;
  f.alpha = alpha;
  f.rho = si.rho;
  return f;
}

// Platt's binary SVM Probabilistic Output: an improvement from Lin et al.
static void
sigmoid_train(
    int l, const double* dec_values, const double* labels, double& A, double& B)
{
  double prior1 = 0, prior0 = 0;

  for (int i = 0; i < l; i++)
    if (labels[i] > 0)
      prior1 += 1;
    else
      prior0 += 1;

  const int max_iter = 100; // Maximal number of iterations

  const double min_step = 1e-10; // Minimal step taken in line search

  const double sigma = 1e-12; // For numerically strict PD of Hessian

  const double eps = 1e-5;

  const double hiTarget = (prior1 + 1.0) / (prior1 + 2.0);

  const double loTarget = 1 / (prior0 + 2.0);

  double* t = Malloc(double, l);

  // Initial Point and Initial Fun Value
  A = 0.0;

  B = std::log((prior0 + 1.0) / (prior1 + 1.0));

  double fval = 0.0;

  for (int i = 0; i < l; i++) {
    if (labels[i] > 0)
      t[i] = hiTarget;
    else
      t[i] = loTarget;

    double fApB = dec_values[i] * A + B;

    if (fApB >= 0)
      fval += t[i] * fApB + std::log(1 + std::exp(-fApB));
    else
      fval += (t[i] - 1) * fApB + std::log(1 + std::exp(fApB));
  }

  int iter = 0;
  for (; iter < max_iter; iter++) {
    // Update Gradient and Hessian (use H' = H + sigma I)
    double h11 = sigma; // numerically ensures strict PD
    double h22 = sigma;
    double h21 = 0.0;
    double g1 = 0.0;
    double g2 = 0.0;

    for (int i = 0; i < l; i++) {
      double fApB = dec_values[i] * A + B;
      double p, q;

      if (fApB >= 0) {
        p = std::exp(-fApB) / (1.0 + std::exp(-fApB));
        q = 1.0 / (1.0 + std::exp(-fApB));
      }
      else {
        p = 1.0 / (1.0 + std::exp(fApB));
        q = std::exp(fApB) / (1.0 + std::exp(fApB));
      }

      double d2 = p * q;

      h11 += dec_values[i] * dec_values[i] * d2;
      h22 += d2;
      h21 += dec_values[i] * d2;
      double d1 = t[i] - p;
      g1 += dec_values[i] * d1;
      g2 += d1;
    }

    // Stopping Criteria
    if (std::abs(g1) < eps && std::abs(g2) < eps)
      break;

    // Finding Newton direction: -inv(H') * g
    double det = h11 * h22 - h21 * h21;

    double dA = -(h22 * g1 - h21 * g2) / det;

    double dB = -(-h21 * g1 + h11 * g2) / det;

    double gd = g1 * dA + g2 * dB;

    double stepsize = 1; // Line Search

    while (stepsize >= min_step) {
      double newA = A + stepsize * dA;
      double newB = B + stepsize * dB;

      // New function value
      double newf = 0.0;

      for (int i = 0; i < l; i++) {
        double fApB = dec_values[i] * newA + newB;

        if (fApB >= 0)
          newf += t[i] * fApB + std::log(1 + std::exp(-fApB));
        else
          newf += (t[i] - 1) * fApB + std::log(1 + std::exp(fApB));
      }

      // Check sufficient decrease
      if (newf < fval + 0.0001 * stepsize * gd) {
        A = newA;
        B = newB;
        fval = newf;
        break;
      }
      stepsize /= 2.0;
    }

    if (stepsize < min_step) {
      info("Line search fails in two-class probability estimates\n");
      break;
    }
  }

  if (iter == max_iter)
    info("Reaching maximal iterations in two-class probability estimates\n");

  free(t);
}

static double
sigmoid_predict(double decision_value, double A, double B)
{
  double fApB = decision_value * A + B;
  // 1-p used later; avoid catastrophic cancellation

  if (fApB >= 0)
    return std::exp(-fApB) / (1.0 + std::exp(-fApB));
  return 1.0 / (1 + std::exp(fApB));
}

// Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
static void
multiclass_probability(int k, double** r, double* p)
{
  const int max_iter = max(100, k);
  double** Q = Malloc(double*, k);
  double* Qp = Malloc(double, k);
  const double eps = 0.005 / k;

  for (int t = 0; t < k; t++) {
    p[t] = 1.0 / k; // Valid if k = 1
    Q[t] = Malloc(double, k);
    Q[t][t] = 0;

    for (int j = 0; j < t; j++) {
      Q[t][t] += r[j][t] * r[j][t];
      Q[t][j] = Q[j][t];
    }

    for (int j = t + 1; j < k; j++) {
      Q[t][t] += r[j][t] * r[j][t];
      Q[t][j] = -r[j][t] * r[t][j];
    }
  }

  int iter = 0;
  for (; iter < max_iter; iter++) {
    // stopping condition, recalculate QP,pQP for numerical accuracy
    double pQp = 0;

    for (int t = 0; t < k; t++) {
      Qp[t] = 0;

      for (int j = 0; j < k; j++)
        Qp[t] += Q[t][j] * p[j];

      pQp += p[t] * Qp[t];
    }

    double max_error = 0;

    for (int t = 0; t < k; t++) {
      double error = std::abs(Qp[t] - pQp);

      if (error > max_error)
        max_error = error;
    }

    if (max_error < eps)
      break;

    for (int t = 0; t < k; t++) {
      double diff = (-Qp[t] + pQp) / Q[t][t];
      p[t] += diff;
      pQp = (pQp + diff * (diff * Q[t][t] + 2 * Qp[t])) / (1 + diff) / (1 + diff);

      for (int j = 0; j < k; j++) {
        Qp[j] = (Qp[j] + diff * Q[t][j]) / (1 + diff);
        p[j] /= (1 + diff);
      }
    }
  }

  if (iter == max_iter)
    info("Exceeds max_iter in multiclass_prob\n");

  for (int t = 0; t < k; t++)
    free(Q[t]);

  free(Q);

  free(Qp);
}

// Cross-validation decision values for probability estimates
static void
svm_binary_svc_probability(const svm_problem* prob,
                           const svm_parameter* param,
                           double Cp,
                           double Cn,
                           double& probA,
                           double& probB)
{
  int nr_fold = 5;
  int* perm = Malloc(int, prob->l);
  double* dec_values = Malloc(double, prob->l);

  // random shuffle

  for (int i = 0; i < prob->l; i++)
    perm[i] = i;

  for (int i = 0; i < prob->l; i++) {
    int j = i + rand() % (prob->l - i);
    swap(perm[i], perm[j]);
  }

  for (int i = 0; i < nr_fold; i++) {
    int begin = i * prob->l / nr_fold;
    int end = (i + 1) * prob->l / nr_fold;

    struct svm_problem subprob;

    subprob.l = prob->l - (end - begin);
    subprob.x = Malloc(struct svm_node*, subprob.l);
    subprob.y = Malloc(double, subprob.l);

    int k = 0;

    for (int j = 0; j < begin; j++) {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      ++k;
    }

    for (int j = end; j < prob->l; j++) {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      ++k;
    }

    int p_count = 0, n_count = 0;

    for (int j = 0; j < k; j++)
      if (subprob.y[j] > 0)
        p_count++;
      else
        n_count++;

    if (p_count == 0 && n_count == 0)
      for (int j = begin; j < end; j++)
        dec_values[perm[j]] = 0;
    else if (p_count > 0 && n_count == 0)
      for (int j = begin; j < end; j++)
        dec_values[perm[j]] = 1;
    else if (p_count == 0 && n_count > 0)
      for (int j = begin; j < end; j++)
        dec_values[perm[j]] = -1;
    else {
      svm_parameter subparam = *param;
      subparam.probability = 0;
      subparam.C = 1.0;
      subparam.nr_weight = 2;
      subparam.weight_label = Malloc(int, 2);
      subparam.weight = Malloc(double, 2);
      subparam.weight_label[0] = +1;
      subparam.weight_label[1] = -1;
      subparam.weight[0] = Cp;
      subparam.weight[1] = Cn;

      struct svm_model* submodel = svm_train(&subprob, &subparam);

      for (int j = begin; j < end; j++) {
        svm_predict_values(submodel, prob->x[perm[j]], &(dec_values[perm[j]]));
        // ensure +1 -1 order; reason not using CV subroutine
        dec_values[perm[j]] *= submodel->label[0];
      }

      svm_free_and_destroy_model(&submodel);

      svm_destroy_param(&subparam);
    }

    free(subprob.x);

    free(subprob.y);
  }

  sigmoid_train(prob->l, dec_values, prob->y, probA, probB);

  free(dec_values);
  free(perm);
}

// Return parameter of a Laplace distribution
static double
svm_svr_probability(const svm_problem* prob, const svm_parameter* param)
{
  int nr_fold = 5;
  double* ymv = Malloc(double, prob->l);
  double mae = 0;

  svm_parameter newparam = *param;
  newparam.probability = 0;
  svm_cross_validation(prob, &newparam, nr_fold, ymv);

  for (int i = 0; i < prob->l; i++) {
    ymv[i] = prob->y[i] - ymv[i];
    mae += std::abs(ymv[i]);
  }

  mae /= prob->l;

  double std = sqrt(2 * mae * mae);
  int count = 0;
  mae = 0;

  for (int i = 0; i < prob->l; i++)
    if (std::abs(ymv[i]) > 5 * std)
      count += 1;
    else
      mae += std::abs(ymv[i]);

  mae /= (prob->l - count);

  info("Prob. model for test data: target value = predicted value + z,\nz: Laplace "
       "distribution e^(-|z|/sigma)/(2sigma),sigma= %g\n",
       mae);

  free(ymv);

  return mae;
}

// label: label name, start: begin of each class, count: #data of classes, perm: indices
// to the original data perm, length l, must be allocated before calling this subroutine
static void
svm_group_classes(const svm_problem* prob,
                  int* nr_class_ret,
                  int** label_ret,
                  int** start_ret,
                  int** count_ret,
                  int* perm)
{
  int l = prob->l;
  int max_nr_class = 16;
  int nr_class = 0;
  int* label = Malloc(int, max_nr_class);
  int* count = Malloc(int, max_nr_class);
  int* data_label = Malloc(int, l);

  for (int i = 0; i < l; i++) {
    int this_label = int(prob->y[i]);
    int j;

    for (j = 0; j < nr_class; j++) {
      if (this_label == label[j]) {
        ++count[j];
        break;
      }
    }

    data_label[i] = j;

    if (j == nr_class) {
      if (nr_class == max_nr_class) {
        max_nr_class *= 2;
        label = static_cast<int*>(realloc(label, max_nr_class * sizeof(int)));
        count = static_cast<int*>(realloc(count, max_nr_class * sizeof(int)));
      }

      label[nr_class] = this_label;

      count[nr_class] = 1;
      ++nr_class;
    }
  }

  int* start = Malloc(int, nr_class);

  start[0] = 0;

  for (int i = 1; i < nr_class; i++)
    start[i] = start[i - 1] + count[i - 1];

  for (int i = 0; i < l; i++) {
    perm[start[data_label[i]]] = i;
    ++start[data_label[i]];
  }

  start[0] = 0;

  for (int i = 1; i < nr_class; i++)
    start[i] = start[i - 1] + count[i - 1];

  *nr_class_ret = nr_class;

  *label_ret = label;

  *start_ret = start;

  *count_ret = count;

  free(data_label);
}

//
// Interface functions
//
svm_model*
svm_train(const svm_problem* prob, const svm_parameter* param)
{
  svm_model* model = Malloc(svm_model, 1);
  model->param = *param;
  model->free_sv = 0; // XXX
  model->probA = nullptr;
  model->probB = nullptr;

  if (param->svm_type == ONE_CLASS || param->svm_type == EPSILON_SVR ||
      param->svm_type == NU_SVR) {
    // regression or one-class-svm
    model->nr_class = 2;
    model->label = nullptr;
    model->nSV = nullptr;
    model->probA = nullptr;
    model->probB = nullptr;
    model->sv_coef = Malloc(double*, 1);

    if (param->probability &&
        (param->svm_type == EPSILON_SVR || param->svm_type == NU_SVR)) {
      model->probA = Malloc(double, 1);
      model->probA[0] = svm_svr_probability(prob, param);
    }

    decision_function f = svm_train_one(prob, param, 0, 0);

    model->rho = Malloc(double, 1);
    model->rho[0] = f.rho;

    int nSV = 0;

    for (int i = 0; i < prob->l; i++)
      if (std::abs(f.alpha[i]) > 0)
        ++nSV;

    model->l = nSV;

    model->SV = Malloc(svm_node*, nSV);

    model->sv_coef[0] = Malloc(double, nSV);

    int j = 0;

    for (int i = 0; i < prob->l; i++)
      if (std::abs(f.alpha[i]) > 0) {
        model->SV[j] = prob->x[i];
        model->sv_coef[0][j] = f.alpha[i];
        ++j;
      }

    free(f.alpha);
  }
  else {
    // classification
    int l = prob->l;
    int nr_class;
    int* label = nullptr;
    int* start = nullptr;
    int* count = nullptr;
    int* perm = Malloc(int, l);

    // group training data of the same class
    svm_group_classes(prob, &nr_class, &label, &start, &count, perm);

    if (nr_class == 1)
      info("WARNING: training data in only one class. See README for details.\n");

    svm_node** x = Malloc(svm_node*, l);

    for (int i = 0; i < l; i++)
      x[i] = prob->x[perm[i]];

    // calculate weighted C

    double* weighted_C = Malloc(double, nr_class);

    for (int i = 0; i < nr_class; i++)
      weighted_C[i] = param->C;

    for (int i = 0; i < param->nr_weight; i++) {
      int j;

      for (j = 0; j < nr_class; j++)
        if (param->weight_label[i] == label[j])
          break;

      if (j == nr_class)
        fprintf(stderr,
                "WARNING: class label %d specified in weight is not found\n",
                param->weight_label[i]);
      else
        weighted_C[j] *= param->weight[i];
    }

    // train k*(k-1)/2 models

    bool* nonzero = Malloc(bool, l);

    for (int i = 0; i < l; i++)
      nonzero[i] = false;

    decision_function* f = Malloc(decision_function, nr_class * (nr_class - 1) / 2);

    double *probA = nullptr, *probB = nullptr;

    if (param->probability) {
      probA = Malloc(double, nr_class*(nr_class - 1) / 2);
      probB = Malloc(double, nr_class*(nr_class - 1) / 2);
    }

    int p = 0;

    for (int i = 0; i < nr_class; i++)
      for (int j = i + 1; j < nr_class; j++) {
        svm_problem sub_prob;
        int si = start[i], sj = start[j];
        int ci = count[i], cj = count[j];
        sub_prob.l = ci + cj;
        sub_prob.x = Malloc(svm_node*, sub_prob.l);
        sub_prob.y = Malloc(double, sub_prob.l);

        for (int k = 0; k < ci; k++) {
          sub_prob.x[k] = x[si + k];
          sub_prob.y[k] = +1;
        }

        for (int k = 0; k < cj; k++) {
          sub_prob.x[ci + k] = x[sj + k];
          sub_prob.y[ci + k] = -1;
        }

        if (param->probability)
          svm_binary_svc_probability(
              &sub_prob, param, weighted_C[i], weighted_C[j], probA[p], probB[p]);

        f[p] = svm_train_one(&sub_prob, param, weighted_C[i], weighted_C[j]);

        for (int k = 0; k < ci; k++)
          if (!nonzero[si + k] && std::abs(f[p].alpha[k]) > 0)
            nonzero[si + k] = true;

        for (int k = 0; k < cj; k++)
          if (!nonzero[sj + k] && std::abs(f[p].alpha[ci + k]) > 0)
            nonzero[sj + k] = true;

        free(sub_prob.x);

        free(sub_prob.y);

        ++p;
      }

    // build output

    model->nr_class = nr_class;

    model->label = Malloc(int, nr_class);

    for (int i = 0; i < nr_class; i++)
      model->label[i] = label[i];

    model->rho = Malloc(double, nr_class*(nr_class - 1) / 2);

    for (int i = 0; i < nr_class * (nr_class - 1) / 2; i++)
      model->rho[i] = f[i].rho;

    if (param->probability) {
      model->probA = Malloc(double, nr_class*(nr_class - 1) / 2);
      model->probB = Malloc(double, nr_class*(nr_class - 1) / 2);

      for (int i = 0; i < nr_class * (nr_class - 1) / 2; i++) {
        model->probA[i] = probA[i];
        model->probB[i] = probB[i];
      }
    }
    else {
      model->probA = nullptr;
      model->probB = nullptr;
    }

    int total_sv = 0;

    int* nz_count = Malloc(int, nr_class);
    model->nSV = Malloc(int, nr_class);

    for (int i = 0; i < nr_class; i++) {
      int nSV = 0;

      for (int j = 0; j < count[i]; j++)
        if (nonzero[start[i] + j]) {
          ++nSV;
          ++total_sv;
        }

      model->nSV[i] = nSV;

      nz_count[i] = nSV;
    }

    info("Total nSV = %d\n", total_sv);

    model->l = total_sv;
    model->SV = Malloc(svm_node*, total_sv);
    p = 0;

    for (int i = 0; i < l; i++)
      if (nonzero[i])
        model->SV[p++] = x[i];

    int* nz_start = Malloc(int, nr_class);

    nz_start[0] = 0;

    for (int i = 1; i < nr_class; i++)
      nz_start[i] = nz_start[i - 1] + nz_count[i - 1];

    model->sv_coef = Malloc(double*, nr_class - 1);

    for (int i = 0; i < nr_class - 1; i++)
      model->sv_coef[i] = Malloc(double, total_sv);

    p = 0;

    for (int i = 0; i < nr_class; i++)
      for (int j = i + 1; j < nr_class; j++) {
        // classifier (i,j): coefficients with
        // i are in sv_coef[j-1][nz_start[i]...],
        // j are in sv_coef[i][nz_start[j]...]

        int si = start[i];
        int sj = start[j];
        int ci = count[i];
        int cj = count[j];

        int q = nz_start[i];

        for (int k = 0; k < ci; k++)
          if (nonzero[si + k])
            model->sv_coef[j - 1][q++] = f[p].alpha[k];

        q = nz_start[j];

        for (int k = 0; k < cj; k++)
          if (nonzero[sj + k])
            model->sv_coef[i][q++] = f[p].alpha[ci + k];

        ++p;
      }

    free(label);

    free(probA);
    free(probB);
    free(count);
    free(perm);
    free(start);
    free(x);
    free(weighted_C);
    free(nonzero);

    for (int i = 0; i < nr_class * (nr_class - 1) / 2; i++)
      free(f[i].alpha);

    free(f);

    free(nz_count);

    free(nz_start);
  }

  return model;
}

// Stratified cross validation
void
svm_cross_validation(const svm_problem* prob,
                     const svm_parameter* param,
                     int nr_fold,
                     double* target)
{
  int* fold_start = Malloc(int, nr_fold + 1);
  int l = prob->l;
  int* perm = Malloc(int, l);
  int nr_class;

  // stratified cv may not give leave-one-out rate
  // Each class to l folds -> some folds may have zero elements

  if ((param->svm_type == C_SVC || param->svm_type == NU_SVC) && nr_fold < l) {
    int* start = nullptr;
    int* label = nullptr;
    int* count = nullptr;
    svm_group_classes(prob, &nr_class, &label, &start, &count, perm);

    // random shuffle and then data grouped by fold using the array perm
    int* fold_count = Malloc(int, nr_fold);
    int* index = Malloc(int, l);

    for (int i = 0; i < l; i++)
      index[i] = perm[i];

    for (int c = 0; c < nr_class; c++)
      for (int i = 0; i < count[c]; i++) {
        int j = i + rand() % (count[c] - i);
        swap(index[start[c] + j], index[start[c] + i]);
      }

    for (int i = 0; i < nr_fold; i++) {
      fold_count[i] = 0;

      for (int c = 0; c < nr_class; c++)
        fold_count[i] += (i + 1) * count[c] / nr_fold - i * count[c] / nr_fold;
    }

    fold_start[0] = 0;

    for (int i = 1; i <= nr_fold; i++)
      fold_start[i] = fold_start[i - 1] + fold_count[i - 1];

    for (int c = 0; c < nr_class; c++)
      for (int i = 0; i < nr_fold; i++) {
        int begin = start[c] + i * count[c] / nr_fold;
        int end = start[c] + (i + 1) * count[c] / nr_fold;

        for (int j = begin; j < end; j++) {
          perm[fold_start[i]] = index[j];
          fold_start[i]++;
        }
      }

    fold_start[0] = 0;

    for (int i = 1; i <= nr_fold; i++)
      fold_start[i] = fold_start[i - 1] + fold_count[i - 1];

    free(start);

    free(label);

    free(count);

    free(index);

    free(fold_count);
  }
  else {
    for (int i = 0; i < l; i++)
      perm[i] = i;

    for (int i = 0; i < l; i++) {
      int j = i + rand() % (l - i);
      swap(perm[i], perm[j]);
    }

    for (int i = 0; i <= nr_fold; i++)
      fold_start[i] = i * l / nr_fold;
  }

  for (int i = 0; i < nr_fold; i++) {
    int begin = fold_start[i];
    int end = fold_start[i + 1];

    struct svm_problem subprob;

    subprob.l = l - (end - begin);
    subprob.x = Malloc(struct svm_node*, subprob.l);
    subprob.y = Malloc(double, subprob.l);

    int k = 0;

    for (int j = 0; j < begin; j++) {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      ++k;
    }

    for (int j = end; j < l; j++) {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      ++k;
    }

    struct svm_model* submodel = svm_train(&subprob, param);

    if (param->probability && (param->svm_type == C_SVC || param->svm_type == NU_SVC)) {
      double* prob_estimates = Malloc(double, svm_get_nr_class(submodel));

      for (int j = begin; j < end; j++)
        target[perm[j]] =
            svm_predict_probability(submodel, prob->x[perm[j]], prob_estimates);

      free(prob_estimates);
    }
    else
      for (int j = begin; j < end; j++)
        target[perm[j]] = svm_predict(submodel, prob->x[perm[j]]);

    svm_free_and_destroy_model(&submodel);

    free(subprob.x);

    free(subprob.y);
  }

  free(fold_start);

  free(perm);
}

int
svm_get_svm_type(const svm_model* model)
{
  return model->param.svm_type;
}

int
svm_get_nr_class(const svm_model* model)
{
  return model->nr_class;
}

void
svm_get_labels(const svm_model* model, int* label)
{
  if (model->label != nullptr)
    for (int i = 0; i < model->nr_class; i++)
      label[i] = model->label[i];
}

double
svm_get_svr_probability(const svm_model* model)
{
  if ((model->param.svm_type == EPSILON_SVR || model->param.svm_type == NU_SVR) &&
      model->probA != nullptr)
    return model->probA[0];
  fprintf(stderr, "Model doesn't contain information for SVR probability inference\n");
  return 0;
}

double
svm_predict_values(const svm_model* model, const svm_node* x, double* dec_values)
{
  if (model->param.svm_type == ONE_CLASS || model->param.svm_type == EPSILON_SVR ||
      model->param.svm_type == NU_SVR) {
    double* sv_coef = model->sv_coef[0];
    double sum = 0;

    for (int i = 0; i < model->l; i++)
      sum += sv_coef[i] * Kernel::k_function(x, model->SV[i], model->param);

    sum -= model->rho[0];

    *dec_values = sum;

    if (model->param.svm_type == ONE_CLASS)
      return (sum > 0) ? 1 : -1;
    return sum;
  }

  int nr_class = model->nr_class;
  int l = model->l;

  double* kvalue = Malloc(double, l);

  for (int i = 0; i < l; i++)
    kvalue[i] = Kernel::k_function(x, model->SV[i], model->param);

  int* start = Malloc(int, nr_class);

  start[0] = 0;

  for (int i = 1; i < nr_class; i++)
    start[i] = start[i - 1] + model->nSV[i - 1];

  int* vote = Malloc(int, nr_class);

  for (int i = 0; i < nr_class; i++)
    vote[i] = 0;

  int p = 0;

  for (int i = 0; i < nr_class; i++)
    for (int j = i + 1; j < nr_class; j++) {
      double sum = 0;
      int si = start[i];
      int sj = start[j];
      int ci = model->nSV[i];
      int cj = model->nSV[j];

      double* coef1 = model->sv_coef[j - 1];
      double* coef2 = model->sv_coef[i];

      for (int k = 0; k < ci; k++)
        sum += coef1[si + k] * kvalue[si + k];

      for (int k = 0; k < cj; k++)
        sum += coef2[sj + k] * kvalue[sj + k];

      sum -= model->rho[p];

      dec_values[p] = sum;

      if (dec_values[p] > 0)
        ++vote[i];
      else
        ++vote[j];

      p++;
    }

  int vote_max_idx = 0;

  for (int i = 1; i < nr_class; i++)
    if (vote[i] > vote[vote_max_idx])
      vote_max_idx = i;

  free(kvalue);
  free(start);
  free(vote);

  return model->label[vote_max_idx];
}

double
svm_predict(const svm_model* model, const svm_node* x)
{
  int nr_class = model->nr_class;
  double* dec_values;

  if (model->param.svm_type == ONE_CLASS || model->param.svm_type == EPSILON_SVR ||
      model->param.svm_type == NU_SVR)
    dec_values = Malloc(double, 1);
  else
    dec_values = Malloc(double, nr_class*(nr_class - 1) / 2);

  double pred_result = svm_predict_values(model, x, dec_values);

  free(dec_values);

  return pred_result;
}

double
svm_predict_probability(const svm_model* model,
                        const svm_node* x,
                        double* prob_estimates)
{
  if ((model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC) &&
      model->probA != nullptr && model->probB != nullptr) {
    int nr_class = model->nr_class;
    double* dec_values = Malloc(double, nr_class*(nr_class - 1) / 2);
    svm_predict_values(model, x, dec_values);

    double min_prob = 1e-7;
    double** pairwise_prob = Malloc(double*, nr_class);

    for (int i = 0; i < nr_class; i++)
      pairwise_prob[i] = Malloc(double, nr_class);

    int k = 0;

    for (int i = 0; i < nr_class; i++)
      for (int j = i + 1; j < nr_class; j++) {
        pairwise_prob[i][j] =
            min(max(sigmoid_predict(dec_values[k], model->probA[k], model->probB[k]),
                    min_prob),
                1 - min_prob);
        pairwise_prob[j][i] = 1 - pairwise_prob[i][j];
        k++;
      }

    multiclass_probability(nr_class, pairwise_prob, prob_estimates);

    int prob_max_idx = 0;

    for (int i = 1; i < nr_class; i++)
      if (prob_estimates[i] > prob_estimates[prob_max_idx])
        prob_max_idx = i;

    for (int i = 0; i < nr_class; i++)
      free(pairwise_prob[i]);

    free(dec_values);

    free(pairwise_prob);

    return model->label[prob_max_idx];
  }
  return svm_predict(model, x);
}

static const char* svm_type_table[] = {
    "c_svc", "nu_svc", "one_class", "epsilon_svr", "nu_svr", nullptr};

static const char* kernel_type_table[] = {
    "linear", "polynomial", "rbf", "sigmoid", "precomputed", nullptr};

int
svm_save_model(const char* model_file_name, const svm_model* model)
{
  FILE* fp = fopen(model_file_name, "we");

  if (fp == nullptr)
    return -1;

  const svm_parameter& param = model->param;

  fprintf(fp, "svm_type %s\n", svm_type_table[param.svm_type]);

  fprintf(fp, "kernel_type %s\n", kernel_type_table[param.kernel_type]);

  if (param.kernel_type == POLY)
    fprintf(fp, "degree %d\n", param.degree);

  if (param.kernel_type == POLY || param.kernel_type == RBF ||
      param.kernel_type == SIGMOID)
    fprintf(fp, "gamma %g\n", param.gamma);

  if (param.kernel_type == POLY || param.kernel_type == SIGMOID)
    fprintf(fp, "coef0 %g\n", param.coef0);

  int nr_class = model->nr_class;

  int l = model->l;

  fprintf(fp, "nr_class %d\n", nr_class);

  fprintf(fp, "total_sv %d\n", l);

  {
    fprintf(fp, "rho");

    for (int i = 0; i < nr_class * (nr_class - 1) / 2; i++)
      fprintf(fp, " %g", model->rho[i]);

    fprintf(fp, "\n");
  }

  if (model->label) {
    fprintf(fp, "label");

    for (int i = 0; i < nr_class; i++)
      fprintf(fp, " %d", model->label[i]);

    fprintf(fp, "\n");
  }

  if (model->probA) // regression has probA only
  {
    fprintf(fp, "probA");

    for (int i = 0; i < nr_class * (nr_class - 1) / 2; i++)
      fprintf(fp, " %g", model->probA[i]);

    fprintf(fp, "\n");
  }

  if (model->probB) {
    fprintf(fp, "probB");

    for (int i = 0; i < nr_class * (nr_class - 1) / 2; i++)
      fprintf(fp, " %g", model->probB[i]);

    fprintf(fp, "\n");
  }

  if (model->nSV) {
    fprintf(fp, "nr_sv");

    for (int i = 0; i < nr_class; i++)
      fprintf(fp, " %d", model->nSV[i]);

    fprintf(fp, "\n");
  }

  fprintf(fp, "scaling ");

  int ii = 0;

  while (model->scaling[ii].index != -1) {
    if (model->scaling[ii].index)
      fprintf(fp, "%d:%.8g ", ii, model->scaling[ii].value);

    ii++;
  }

  fprintf(fp, "\n");

  fprintf(fp, "SV\n");
  const double* const* sv_coef = model->sv_coef;
  const svm_node* const* SV = model->SV;

  for (int i = 0; i < l; i++) {
    for (int j = 0; j < nr_class - 1; j++)
      fprintf(fp, "%.16g ", sv_coef[j][i]);

    const svm_node* p = SV[i];

    if (param.kernel_type == PRECOMPUTED)
      fprintf(fp, "0:%d ", int(p->value));
    else
      while (p->index != -1) {
        fprintf(fp, "%d:%.8g ", p->index, p->value);
        p++;
      }

    fprintf(fp, "\n");
  }

  if (ferror(fp) != 0 || fclose(fp) != 0)
    return -1;
  return 0;
}

static char* line = nullptr;
static int max_line_len;

static char*
readline(FILE* input)
{
  if (fgets(line, max_line_len, input) == nullptr)
    return nullptr;

  while (strrchr(line, '\n') == nullptr) {
    max_line_len *= 2;
    line = static_cast<char*>(realloc(line, max_line_len));
    int len = int(strlen(line));

    if (fgets(line + len, max_line_len - len, input) == nullptr)
      break;
  }

  return line;
}

svm_model*
svm_load_model(const char* model_file_name)
{
  FILE* fp = fopen(model_file_name, "rbe");

  if (fp == nullptr)
    return nullptr;

  // read parameters

  svm_model* model = Malloc(svm_model, 1);

  svm_parameter& param = model->param;

  model->rho = nullptr;

  model->probA = nullptr;

  model->probB = nullptr;

  model->label = nullptr;

  model->nSV = nullptr;

  model->scaling = Malloc(struct svm_node, 1);

  model->scaling[0].index = -1;

  char cmd[81];

  while (true) {
    int res = fscanf(fp, "%80s", cmd);

    if (res > 0 && strcmp(cmd, "svm_type") == 0) {
      res = fscanf(fp, "%80s", cmd);

      int i = 0;
      for (i = 0; svm_type_table[i]; i++) {
        if (res > 0 && strcmp(svm_type_table[i], cmd) == 0) {
          param.svm_type = i;
          break;
        }
      }

      if (svm_type_table[i] == nullptr) {
        fprintf(stderr, "unknown svm type.\n");
        free(model->rho);
        free(model->label);
        free(model->nSV);
        free(model->scaling);
        free(model);
        return nullptr;
      }
    }
    else if (res > 0 && strcmp(cmd, "kernel_type") == 0) {
      res = fscanf(fp, "%80s", cmd);

      int i = 0;
      for (i = 0; kernel_type_table[i]; i++) {
        if (res > 0 && strcmp(kernel_type_table[i], cmd) == 0) {
          param.kernel_type = i;
          break;
        }
      }

      if (kernel_type_table[i] == nullptr) {
        fprintf(stderr, "unknown kernel function.\n");
        free(model->rho);
        free(model->label);
        free(model->nSV);
        free(model->scaling);
        free(model);
        return nullptr;
      }
    }
    else if (res > 0 && strcmp(cmd, "degree") == 0)
      res = fscanf(fp, "%d", &param.degree);
    else if (res > 0 && strcmp(cmd, "gamma") == 0)
      res = fscanf(fp, "%lf", &param.gamma);
    else if (res > 0 && strcmp(cmd, "coef0") == 0)
      res = fscanf(fp, "%lf", &param.coef0);
    else if (res > 0 && strcmp(cmd, "nr_class") == 0)
      res = fscanf(fp, "%d", &model->nr_class);
    else if (res > 0 && strcmp(cmd, "total_sv") == 0)
      res = fscanf(fp, "%d", &model->l);
    else if (res > 0 && strcmp(cmd, "rho") == 0) {
      int n = model->nr_class * (model->nr_class - 1) / 2;
      model->rho = Malloc(double, n);

      for (int i = 0; (i < n) && (res > 0); i++)
        res = fscanf(fp, "%lf", &model->rho[i]);
    }
    else if (res > 0 && strcmp(cmd, "label") == 0) {
      int n = model->nr_class;
      model->label = Malloc(int, n);

      for (int i = 0; (i < n) && (res > 0); i++)
        res = fscanf(fp, "%d", &model->label[i]);
    }
    else if (res > 0 && strcmp(cmd, "probA") == 0) {
      int n = model->nr_class * (model->nr_class - 1) / 2;
      model->probA = Malloc(double, n);

      for (int i = 0; (i < n) && (res > 0); i++)
        res = fscanf(fp, "%lf", &model->probA[i]);
    }
    else if (res > 0 && strcmp(cmd, "probB") == 0) {
      int n = model->nr_class * (model->nr_class - 1) / 2;
      model->probB = Malloc(double, n);

      for (int i = 0; (i < n) && (res > 0); i++)
        res = fscanf(fp, "%lf", &model->probB[i]);
    }
    else if (res > 0 && strcmp(cmd, "nr_sv") == 0) {
      int n = model->nr_class;
      model->nSV = Malloc(int, n);

      for (int i = 0; (i < n) && (res > 0); i++)
        res = fscanf(fp, "%d", &model->nSV[i]);
    }
    else if (res > 0 && strcmp(cmd, "scaling") == 0) {
      char *idx, buff[10000];
      int ii = 0;
      // char delims[]="\t: ";
      model->scaling = Malloc(struct svm_node, 1);
      res = fscanf(fp, "%10000[^\n]", buff);
      if (res <= 0)
        continue;
      idx = strtok(buff, ":");

      while (idx != nullptr) {
        char* val = strtok(nullptr, " \t");
        int pre_ii = ii;
        ii = atoi(idx);

        model->scaling = Realloc(model->scaling, struct svm_node, ii + 2);

        // setting to zero the non defined scaling factors

        for (int j = pre_ii + 1; j < ii; j++) {
          model->scaling[j].index = 0;
          model->scaling[j].value = 0;
        }

        model->scaling[ii].index = 1;

        model->scaling[ii].value = atof(val);
        ++ii;
        idx = strtok(nullptr, ":");
        // printf("%d e %f\n",model->scaling[ii-1].index,model->scaling[ii-1].value);
      }

      model->scaling[ii].index = -1;
    }
    else if (res > 0 && strcmp(cmd, "SV") == 0) {
      // std::cout << cmd << std::endl;
      while (true) {
        int c = getc(fp);

        if (c == EOF || c == '\n')
          break;
      }

      break;
    }
    else {
      fprintf(stderr, "unknown text in model file: [%s]\n", cmd);
      free(model->rho);
      free(model->label);
      free(model->nSV);
      free(model->scaling);
      free(model);
      return nullptr;
    }
    pcl::utils::ignore(res); // to inform clang-tidy to ignore the dead-stores
  }

  // read sv_coef and SV

  int elements = 0;

  long pos = ftell(fp);

  max_line_len = 10000;

  line = Malloc(char, max_line_len);

  while (readline(fp) != nullptr) {
    strtok(line, ":");

    while (true) {
      char* p = strtok(nullptr, ":");

      if (p == nullptr)
        break;

      ++elements;
    }
  }

  elements += model->l;

  fseek(fp, pos, SEEK_SET);

  int m = model->nr_class - 1;
  int l = model->l;
  model->sv_coef = Malloc(double*, m);

  for (int i = 0; i < m; i++)
    model->sv_coef[i] = Malloc(double, l);

  model->SV = Malloc(svm_node*, l);

  svm_node* x_space = nullptr;

  if (l > 0)
    x_space = Malloc(svm_node, elements);

  long int j = 0;

  for (int i = 0; i < l; i++) {
    readline(fp);
    model->SV[i] = &x_space[j];

    char* p = strtok(line, " \t");
    model->sv_coef[0][i] = strtod(p, nullptr);

    for (int k = 1; k < m; k++) {
      p = strtok(nullptr, " \t");
      model->sv_coef[k][i] = strtod(p, nullptr);
    }

    int jj = 0;

    while (true) {
      char* idx = strtok(nullptr, ":");
      char* val = strtok(nullptr, " \t");

      if (val == nullptr)
        break;

      x_space[j].index = int(strtol(idx, nullptr, 10));

      x_space[j].value = strtod(val, nullptr);

      //             printf("i=%d, j=%d, %f ,%d e %f\n",i,j,model->sv_coef[0][i],
      //                    model->SV[i][jj].index, model->SV[i][jj].value);
      jj++;

      ++j;
    }

    x_space[j++].index = -1;
  }

  free(line);

  // printf("%d e %f\n",model->scaling[j-2].index,model->scaling[j-2].value);

  if (ferror(fp) != 0 || fclose(fp) != 0) {
    free(model->rho);
    free(model->label);
    free(model->nSV);
    free(model->scaling);
    free(model);
    return nullptr;
  }

  model->free_sv = 1; // XXX

  return model;
}

void
svm_free_model_content(svm_model* model_ptr)
{
  if (model_ptr->free_sv && model_ptr->l > 0 && model_ptr->SV != nullptr)
    free(static_cast<void*>(model_ptr->SV[0]));

  if (model_ptr->sv_coef) {
    for (int i = 0; i < model_ptr->nr_class - 1; i++)
      free(model_ptr->sv_coef[i]);
  }

  free(model_ptr->SV);

  model_ptr->SV = nullptr;

  free(model_ptr->sv_coef);
  model_ptr->sv_coef = nullptr;

  free(model_ptr->rho);
  model_ptr->rho = nullptr;

  free(model_ptr->label);
  model_ptr->label = nullptr;

  free(model_ptr->probA);
  model_ptr->probA = nullptr;

  free(model_ptr->probB);
  model_ptr->probB = nullptr;

  free(model_ptr->nSV);
  model_ptr->nSV = nullptr;
}

void
svm_free_and_destroy_model(svm_model** model_ptr_ptr)
{
  if (model_ptr_ptr != nullptr && *model_ptr_ptr != nullptr) {
    svm_free_model_content(*model_ptr_ptr);
    free(*model_ptr_ptr);
    *model_ptr_ptr = nullptr;
  }
}

void
svm_destroy_param(svm_parameter* param)
{
  free(param->weight_label);
  free(param->weight);
}

const char*
svm_check_parameter(const svm_problem* prob, const svm_parameter* param)
{
  // svm_type

  int svm_type = param->svm_type;

  if (svm_type != C_SVC && svm_type != NU_SVC && svm_type != ONE_CLASS &&
      svm_type != EPSILON_SVR && svm_type != NU_SVR)
    return "unknown svm type";

  // kernel_type, degree

  int kernel_type = param->kernel_type;

  if (kernel_type != LINEAR && kernel_type != POLY && kernel_type != RBF &&
      kernel_type != SIGMOID && kernel_type != PRECOMPUTED)
    return "unknown kernel type";

  if (param->gamma < 0)
    return "gamma < 0";

  if (param->degree < 0)
    return "degree of polynomial kernel < 0";

  // cache_size,eps,C,nu,p,shrinking

  if (param->cache_size <= 0)
    return "cache_size <= 0";

  if (param->eps <= 0)
    return "eps <= 0";

  if (svm_type == C_SVC || svm_type == EPSILON_SVR || svm_type == NU_SVR)
    if (param->C <= 0)
      return "C <= 0";

  if (svm_type == NU_SVC || svm_type == ONE_CLASS || svm_type == NU_SVR)
    if (param->nu <= 0 || param->nu > 1)
      return "nu <= 0 or nu > 1";

  if (svm_type == EPSILON_SVR)
    if (param->p < 0)
      return "p < 0";

  if (param->shrinking != 0 && param->shrinking != 1)
    return "shrinking != 0 and shrinking != 1";

  if (param->probability != 0 && param->probability != 1)
    return "probability != 0 and probability != 1";

  if (param->probability == 1 && svm_type == ONE_CLASS)
    return "one-class SVM probability output not supported yet";

  // check whether nu-svc is feasible

  if (svm_type == NU_SVC) {
    int l = prob->l;
    int max_nr_class = 16;
    int nr_class = 0;
    int* label = Malloc(int, max_nr_class);
    int* count = Malloc(int, max_nr_class);

    for (int i = 0; i < l; i++) {
      int this_label = int(prob->y[i]);
      int j;

      for (j = 0; j < nr_class; j++)
        if (this_label == label[j]) {
          ++count[j];
          break;
        }

      if (j == nr_class) {
        if (nr_class == max_nr_class) {
          max_nr_class *= 2;
          label = static_cast<int*>(realloc(label, max_nr_class * sizeof(int)));
          count = static_cast<int*>(realloc(count, max_nr_class * sizeof(int)));
        }

        label[nr_class] = this_label;

        count[nr_class] = 1;
        ++nr_class;
      }
    }

    for (int i = 0; i < nr_class; i++) {
      int n1 = count[i];

      for (int j = i + 1; j < nr_class; j++) {
        int n2 = count[j];

        if (param->nu * (n1 + n2) / 2 > min(n1, n2)) {
          free(label);
          free(count);
          return "specified nu is infeasible";
        }
      }
    }

    free(label);

    free(count);
  }

  return nullptr;
}

int
svm_check_probability_model(const svm_model* model)
{
  return ((model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC) &&
          model->probA != nullptr && model->probB != nullptr) ||
         ((model->param.svm_type == EPSILON_SVR || model->param.svm_type == NU_SVR) &&
          model->probA != nullptr);
}

void
svm_set_print_string_function(void (*print_func)(const char*))
{
  if (print_func == nullptr)
    svm_print_string = &print_string_stdout;
  else
    svm_print_string = print_func;
}

#endif // _LIBSVM_HPP_
